Seller reputation, information signals, and prices for heterogeneous coins on eBay.

Alm, James

1. Introduction

It has long been recognized that a market with asymmetrically distributed information may experience a market failure (Akerlof 1970). This insight is especially relevant for the rapidly expanding area of online commerce, where information is not uniformly distributed between the buyer and the seller. In online transactions, the buyer cannot examine the product directly and has to rely upon the seller's description of the product and upon the accuracy of any such description; the buyer also has to rely upon the seller for compliance with the terms of transaction. However, it may be the case that the past reputation of the seller may act as a mechanism by which information about the current behavior of the seller can be transmitted to the buyer. In such a setting, a seller's reputation may well reduce information asymmetries and thereby allow the market to function. For heterogeneous goods in particular, where product characteristics vary significantly from one good to another and where there is much uncertainty about the quality of the goods, it seems likely that a seller's reputation and other information measures may play an especially important role in persuading buyers to participate in a market. In this paper we examine the impact of seller reputation and various information variables on buyers' willingness to pay for a heterogeneous good sold via Interact auctions, using U.S. silver Morgan dollar coins in "Almost Uncirculated" condition that are sold on eBay. We find consistent evidence that a seller's overall reputation has a positive and statistically significant impact on a buyer's willingness to pay, and that negative comments about a seller often have a negative impact on price. Importantly, these reputational effects tend to increase in importance when there is more uncertainty about the quality of the coin.

With some exceptions (McDonald and Slawson 2002), theoretical models have typically generated a positive relationship between the reputation of the seller and the resulting price of the transaction, in large part because the seller's reputation is a proxy for quality characteristics that are unobserved prior to the completion of the transaction (Klein and Leffler 1981; Shapiro 1983; Allen 1984; Houser and Wooders 2000). Experimental findings have also tended to support the theoretical conclusions (DeJong, Forsythe, and Lundholm 1985; Miller and Plott 1985; Camerer and Weigelt 1988; Holt and Sherman 1990). However, until recently empirical analysis of this issue has been limited because of the absence of reliable measures of reputation.

The rapid growth of e-commerce, in combination with the establishment of reputation measures by many consumer-to-consumer Web sites, has now enabled researchers to analyze the issue empirically. (1) Online consumer-to-consumer auction Web sites such as eBay.com, Yahoo.com, and Amazon.com provide a unique opportunity to study the effects of a seller's reputation in the online environment. (2) The most recognized of these Web sites is eBay. It has experienced rapid growth in its user base since its birth in September 1995, and by April 2005 its confirmed registered user base had surpassed 147 million (including 60 million active users). (3) These Web sites assume no responsibility for the items listed on their sites and simply act as auctioneers. The seller assumes full responsibility for the description of the product and for the compliance with the terms of transaction. Of special note, in almost all instances the shipment of the product occurs after the payment is received so the buyer assumes a risk when sending a payment. (4) For instance, the seller may ship a damaged item, may not correctly describe the product in the auction, or may not send the item at all.

However, most online auction Web sites, including eBay, have set up a mechanism that allows buyers to rate the seller and to post short comments about their experience with the seller following the completion of their transaction. (5) The feedback system used by eBay enables the buyer to classify any comment about the seller as positive, negative, or neutral, and the difference between the number of positive and negative comments left by unique buyers constitutes the seller's rating. This rating is then displayed prominently on every auction presented by this seller. Each visitor to the seller's auction can also examine the rating in more detail, including the breakdown of the rating in terms of its positive, negative, and neutral comments. The comments themselves are also available, and vary from praises like "Excellent seller, friendly communications, Thank You!" to warnings aimed at other perspective buyers, such as "Collected payment, never shipped the item, avoid this seller." (6) If information on the seller's reputation can reduce information asymmetries, then such mechanisms may play an important role in facilitating the growth of these Web sites.

Indeed, anecdotal evidence suggests that reputation matters in online auctions. For example, an individual seller brought a $2.6 million suit against both eBay.com and a buyer for negative comments posted by the buyer about the quality of the services provided by the seller (Grace v. eBay, Inc., now settled). More generally, several empirical studies have used data generated by online auction Web sites, including these various measures of reputation, to examine the impact of a seller's reputation and other informational variables on buyers' willingness to pay for auction goods. Although the magnitudes of the impacts of reputation measures vary significantly across these studies, in part due to the variety in the choices of the products across these studies and in part due to the choices of control variables, the emerging consensus is that there exists a statistically significant relationship between the seller's reputation and the buyer's willingness to pay. Houser and Wooders (2000), Dewan and Hsu (2001), Kalyanam and McIntyre (2001), McDonald and Slawson (2002), and Melnik and Alm (2002) all find a positive and statistically significant relationship between the seller's overall reputation and the buyers' willingness to pay; these studies also sometimes find that negative reputation indicators (e.g., the number of complaints) have a negative and statistically significant impact on willingness to pay. (7) Other empirical evidence also suggests that the overall reputation of the seller may not be statistically significant, but that negative reputation plays an important role in the determination of the buyer's willingness to pay (Lucking-Reiley et al. 1999). (8)

One of the key aspects in all of these studies is the choice of the product for such analysis. Almost all of the existing literature on the effects of reputation in online auctions is based on homogeneous, or standardized, goods. For example, Lucking-Reiley et al. (1999) examine U.S. Indian head pennies with grades in near mint state, Houser and Wooders (2000) examine willingness to pay for a Pentium III, 500-MHz processor, Resnick and Zeckhouser (2002) use Rio MP3 digital audio players and Britannia Beanie Babies in mint condition, and Melnik and Alm (2002) choose a mint condition U.S. $5 coin. (9) The selection of a homogeneous good allows the researcher to better control for the characteristics of the product (e.g., its book value), and so to better capture the signaling aspects of the seller's reputation. Nevertheless, the role of the seller's reputation in such a setting seems likely to be somewhat limited because there is little if any variation in the quality of a homogeneous good. In contrast, a heterogeneous good is one for which there remain characteristics of the good that are uncertain for the buyer but that may well affect the buyer's willingness to pay, even in the presence of verifiable components of the good's description (e.g., a visual scan or a grade from a professional grading service). For such goods, a seller-provided description of the product may become more important to a buyer unable to determine the precise quality of the auctioned good, so reputation may play a stronger role with a heterogeneous good than with a homogeneous good; seller reputation may also give some indication of the reliability of the seller in providing the correct description of those item-specific characteristics. As noted by Bajari and Hortacsu (2004), "[w]hen the item is ... used, and has uncertain quality, such as a hard-to-appraise antique, reputation might play a more important role." However, this notion is largely untested. (10)

In this paper we examine buyers' willingness to pay for a heterogeneous product (U.S. silver Morgan dollar coins in "Almost Uncirculated" condition), using data collected from eBay.com. We estimate the impact of the seller's reputation on buyers' willingness to pay for these coins by including the Web site's own measures of the seller's reputation. We also estimate the impact of a variety of other informational variables and auction characteristics that allow us to vary the degree of uncertainty about item-specific characteristics, including separate variables for the presence or absence of visual scans of the coin and for certification of the coin's quality by a credible third party. We find that a seller's overall reputation typically has a positive and statistically significant effect on the willingness of buyers to pay for the good, a result that is robust across a wide range of alternative specifications and alternative subsets of our data. A negative rating for a seller is also often shown to have an important--and negative--impact on willingness to pay. Importantly, however, these reputational effects tend to vary with the degree of uncertainty about the quality of the good. "Certified" coins are likely to have little uncertainty about item-specific characteristics because the quality of the coin is examined by a reliable third party who assigns a precise numerical grade to the coin; "noncertified" coins are likely to have somewhat more uncertainty, especially if they are not accompanied by a visual scan, but the presence of a scan enables the buyer to make an independent judgment about the item-specific characteristics. Put differently, certified coins tend to be more homogeneous than noncertified coins, and noncertified coins with a scan tend to be more homogeneous than noncertified coins without a scan. Indeed, when we examine separately the various subsets of our data (e.g., noncertified coins only, certified coins only, and noncertified coins with and without visual scans), our results show that both the magnitude of the seller's reputation effect and its statistical significance generally increase with the degree of uncertainty about the item-specific characteristics; that is, the coefficient estimates of the reputation measures tend to be larger for noncertified than for certified coins, and larger also for noncertified coins without a visual scan. Reputation therefore seems to matter more for more heterogeneous goods, when there is more uncertainty about the quality of the coin.

In the next section we discuss our basic framework, our data, and our empirical methods. In Section 3 we present our estimation results. We conclude with a summary and some implications of our results.

2. Analytical Framework, Data, and Empirical Methods

Analytical Framework

It is straightforward to show that a seller's reputation can have a positive impact on a buyer's willingness to pay. For example, Houser and Wooders (2000) assume an auction with honest and dishonest sellers, in which the honest seller always delivers the promised good after receipt of the payment and the dishonest seller never delivers the good. They assume that a seller's reputation can be measured by the probability that the seller is honest, which they term his or her reputation score. If this information is assumed to be publicly available, it is then straightforward to show that the expected utility of any buyer is an increasing function in the reputation score of the seller, and the buyer is willing to pay more when the reputation score is higher. (11) Klein and Leffler (1981), Shapiro (1983), and Allen (1984) derive a similar conclusion.

Perhaps surprisingly, however, it is also possible to construct models in which reputation provides no information and is useless. McDonald and Slawson (2002) assume that reputation is needed to provide sellers with an incentive to provide high quality service. However, the reputation score itself provides little information about seller quality because in equilibrium all sellers will choose to be high quality.

The actual impact of reputation on selling price is therefore an empirical issue. Following the approaches of Lucking-Reiley et al. (1999), Houser and Wooders (2000), Dewan and Hsu (2001), Kalyanam and McIntyre (2001), and McDonald and Slawson (2002), we assume that the price of the coin depends upon a vector of characteristics (X) that includes the seller's reputation and other information signals, the market value of the coin, and the auction features.

Data

A first issue that must be addressed when analyzing private auctions like the ones displayed on eBay.com is the heterogeneity of the product. Most of the items sold on eBay tend to be relatively heterogeneous in nature; that is, these items tend to be ones for which there remain characteristics of the good that are uncertain for the buyer, even when verifiable components of the good's description are provided by the seller. This heterogeneity is typically captured in the seller's description of the item, thereby signaling to the buyer information on item-specific characteristics, and prices can vary significantly between auctions for the same good because of variations in quality. In contrast, with homogeneous goods, the standardized nature of the good largely eliminates quality differences between items offered by different sellers.

Accounting for heterogeneity is difficult. Accordingly, we select a good that satisfies two criteria. First, the item must be graded by the seller based on some standardized and generally accepted scale. Second, information about any item-specific quality characteristics of the item must be captured by any such grading scale. The first requirement is essential in order to have a measure that allows a comparison across different auctions listed by different sellers, and the second requirement assures that such a measure captures item-specific characteristics.

Collectible coins satisfy both criteria. Coins are graded on a widely accepted standard scale, with coin grading varying from "mint" state (or "Uncirculated" condition) to "good" (where hardly any detail on the surface of the coin remains visible). Coins in mint condition can be considered as perfectly homogeneous goods, while coins in less than mint condition can exhibit substantial heterogeneity. This heterogeneity of collectible coins arises from variation in item-specific characteristics. Unless the coin is certified, it is the seller's responsibility to adequately represent the grade of the coin in the description of the item offered for sale. Furthermore, the grade represents the opinion of the seller, and it is possible that the seller may incorrectly grade the coin. For example, the seller may state that the coin is in "Almost Uncirculated" (AU) grade when in reality the grade of the coin may be lower, such as "Extremely Fine" (EF). Because the value of the coin is largely based on the condition of the coin, any such misrepresentation of the grade can significantly impact the buyer's valuation of the coin. (12) Under these conditions the buyer is forced to rely on the seller for the accuracy of the description of the item. Note that this problem would not arise in the case of perfectly homogeneous items (e.g., certified coins or coins in mint condition), where either the item-specific characteristics are fully known to all parties (certified coins) or there is no variation in item-specific characteristics (mint condition coins).

Coins in less than mint condition allow for an analysis of the impact of reputation and other information signals on the prices of heterogeneous goods. For these reasons, we use U.S. Morgan silver dollar coins in "Almost Uncirculated" (AU) condition for this study. (13) Morgan dollars were minted in the U.S. between 1878 and 1904 and in 1921, and are very popular among U.S. coin collectors. (14) We collected observations from the online auction Web site eBay.com between August 1, 2002, and September 30, 2002. In total, our dataset consists of 3828 observations, generated by 639 unique sellers. (15) The average price (Price) for completed auctions in the dataset is $93.39, and it is Price that is the dependent variable in all of our specifications. (16) Table 1 provides detailed summary statistics for Price, as well as for all other variables in the dataset.

There are several variables that may affect the price of the coins. Our primary interest is in the impact of the seller's reputation on the buyer's willingness to pay. Reputation is measured by the overall rating of the seller (Rating), calculated as the difference between positive and negative comments left by unique users who have completed a transaction with the seller. Rating has a mean value of 1889, and it exhibits substantial variation, ranging from a minimum value of 0 to a maximum value of 13, 890. The information contained in Rating is also used to construct two additional reputation variables. One focuses more precisely on the negative rating of the seller (Negative), and is equal to the number of feedback responses from unique users that rate the seller as negative. In addition, a measure Neutral is included, equal to the number of neutral comments about the seller left by unique users.

Our expectation is that Rating will have a positive impact on the auction price, while Negative will have a negative impact and Neutral seems likely to have a negative impact as well. However, our measures of reputation are likely to be somewhat imperfect indicators, for several reasons. Not every transaction results in a feedback comment because there is little economic motivation for buyers to provide feedback after a transaction has been completed. Also, there are no real standards to distinguish deliberate seller fraud from honest mistakes, the measures do not provide a complete indicator of seller quality, and sellers (and buyers) may attempt to manipulate the measures, perhaps by changing their Internet identities. Note that, even though bidders can see all of the seller's feedback information, they do not know the total number of transactions completed by the seller.

Aside from these three direct indicators of reputation, there are several other channels by which information signals may be transmitted to buyers. Our dataset consists of "certified" and "noncertified" coins. "Certified" coins receive a grade by a third party professional grading service (e.g., the Professional Coin Grading Service, or PCGS), of which only seven operate in the United States. Once a coin is graded by one of these professional grading companies, the coin is sealed in a plastic holder, along with precise grading information. These grades are assigned in a numerical form, with a higher number representing a better coin quality. Four such numerical grades are present in our dataset: AU-50, AU-53, AU-55, and AU-58, with AU-58 coins being of the highest quality and AU-50 the lowest. All of these coins fall into the broadly defined AU grade category. (17) In contrast, among "noncertified" coins a numerical grading is very uncommon, and, even when present, a grading is offered only as an opinion of the seller. Because certification of a coin may serve as a signal of the quality of the coin, as well as a verification that the coin is not fake, one would expect that certified coins would command higher valuation. Perhaps even more important, certification clearly reduces, if not completely eliminates, uncertainty about the quality of the coin. Consequently, although certification should not necessarily eliminate the impact of the seller's reputation on price, it does seem likely to restrict the role of reputation to that of an indicator of the reliability of the seller when it comes to compliance with the terms of the transaction, similar to its effects for homogeneous goods. In contrast, with noncertified coins, the buyer may view the seller's reputation as an indicator of the probability that the seller is providing an accurate description of item-specific details (as well as an indicator that the seller will comply with the transaction). In a first set of regressions in which all coins are included (denoted "Estimation Results I"), we include a dummy variable (Certified), equal to 1 if the coin is certified and 0 otherwise. Our expectation is that Certified should have a positive impact on Price.

Importantly, we also investigate the effects of reputational measures in auctions of noncertified and certified coins separately (Estimation Results II and III, respectively). (18) If certification reduces uncertainty about the quality of the coin, then the impact of Rating on the willingness to pay for certified coins should be significantly reduced relative to its impact on noncertified coins, and limited mainly to that of an indicator about the reliability of the seller in complying with the terms of the transaction.

Because the value of the coin is expected to be a function of its condition, we include dummy variables for each numerical grade category in all three sets of regressions. These grades also provide information signals, and our expectation is that coins of higher grades will realize higher prices; however, the professional rating service PCGS provides no market values for each of these numerical categories, even though PCGS lists market values for all Morgan dollar coins on its Web site.

Other information signals provide additional channels of information transmission. Even in the absence of certification, a visual scan of the coin allows buyers to make their own judgments about the item-specific characteristics of the coin. This visual description of the coin is represented by two dummy variables: FullScan, equal to 1 when scans of both sides of the actual coin offered for sale are present and 0 otherwise, and PartialScan, equal to 1 when a scan of only one side of the coin is provided and 0 otherwise. These visual descriptions are included in all three sets of regressions. In addition, we restrict our sample to noncertified coins only (Estimation Results IV) and perform separate estimations on these noncertified coins with and without the visual description present in the auction. In the case of certified coins, little uncertainty exists about item-specific characteristics, and a visual description is expected to play a limited role; in contrast, for noncertified coins the visual description is likely to be important.

A number of other control variables are included in the estimations. Our dataset consists of observations on coins minted in different years and with different "mint marks." (19) To account for the differences in coin value based on the year and the mint mark, we include a variable CoinValue, which represents the market value of the coin in AU grade as of September 2002, obtained from the PCGS Web site. (20)

We include several variables that reflect the features of the auction. Three of these relate to the acceptable methods of payment by the seller, and are entered as dummy variables: CreditCard, equal to 1 if the seller accepts credit cards directly and 0 otherwise; PersonalCheck, equal to 1 if the seller accepts personal checks and 0 otherwise; and OnlinePayment, equal to 1 if any online payment method (e.g., PayPal, BidPay, Billpoint, C2it) is an acceptable method of payment and 0 otherwise. (21) No sellers in our dataset allows cash-on-delivery (COD) as a payment option. However, a large number list multiple options for the method of payment. For example, looking at all the sellers in our dataset, all sellers accept money orders, many sellers (89%) accept personal checks, 77% accept online methods of payment, and 13% allow payment via credit cards. These various methods have different benefits and costs, both for buyers and sellers. Unlike money orders, personal checks have lower transaction costs because checks do not require a trip to the U.S. Post Office to purchase a money order and they do not have any additional monetary costs associated with money orders. However, use of personal checks will almost always result in a delay in the shipping of the item by the seller because, in all instances in which the seller accepts a personal check, the seller requires that the check clear prior to shipping the item. In contrast, acceptance of online payment methods may speed up the shipping and hence the delivery of the item; online methods of payment are also more convenient for the buyer because the payment can be made from a home personal computer. Credit card acceptance by a seller may also act as a signal that the seller has an established business, and the credit card issuer may provide some protection against seller fraud. Both should increase buyers' willingness to pay. There is no information about the actual method of payment chosen by the winning bidder. We have no information in our dataset on whether the seller offered any type of money back guarantee, whether any of the winning bidders attempted to return their coins to the sellers, or whether any winning bidder communicated with the seller during or after the auction.

The time and the day of the week when the auction closes may influence the selling price as well. eBay allows bidders to view a complete list of all current auctions in any category, based on a search query. Such lists can be very large and can involve thousands of individual listings. However, eBay allows bidders to narrow the list based on the remaining time of the auction. Bidders can select to view the list of auctions in their requested category (or to search results) that are closing in the next 24 hours or in the next 4 hours. Importantly, auctions that are near their closing time appear on the top of the search results page in their category. This feature suggests that auctions closing at the time when more bidders visit the eBay Web site may receive higher attention from bidders and so realize higher prices. To investigate this issue, we include dummy variables for four 6-hour periods and also dummy variables for the days of the week. Closing auction time is entered according to the Pacific time zone.

The length of the auction in days (Length) may have an impact on price, because the longer the auction remains active the greater is the likelihood that the auction will be visited by a larger number of bidders and hence realize a higher price. Currently, eBay has four different settings for the choice of the duration of the auction: 3, 5, 7, and 10 days. It is worth noting that in 2001 eBay introduced an additional fee for inserting 10-day auctions, which may signal that eBay expects longer auctions to bring higher prices.

Another factor that may influence the realized price is the supply of coins. Supply variables have typically been ignored in most auction research. To incorporate some supply of coins considerations, we introduce CoinFrequency, defined as the number of auctions of the coin (determined by year and mint) that close at the same day as the auction in the observation. The closing date is chosen, rather than any other day of the auction, because auctions that are near their closing time appear on the top of the search results page in their category. (22)

We estimate a wide variety of different specifications. In all models the dependent variable is Price, entered in linear form. The reputation variables--Rating, Negative, and Neutral--are all entered in natural log form because the marginal effects of additional feedback points are expected to decrease with reputation. Because the range for the reputation measures begins at 0, the natural logarithm is taken of the value of the variable +1. Other variables are entered in linear form. (23)

Empirical Methods

Many observations are either right- or left-censored. When an auction is inserted on eBay by a seller, the seller is required to specify an opening bid; in some cases, this opening bid exceeds any buyer's willingness to pay and the auction receives no bids. When this happens, an observation is left-censored. Out of 3828 observations, 1283 observations are left-censored.

Further, eBay introduced in 2001 a fixed price mechanism, referred to as BuyItNow. This option enables the sellers to list a specific price at which the auction would end if the first bidder chooses to accept that price; if the first bidder does not choose the BuyItNow price and places a bid instead, then the auction begins and the BuyItNow option disappears. The incentive to the bidder for using the BuyItNow mechanism is obvious because the auction may take the price above the specified price. However, if the BuyItNow option is used by the first bidder, thereby ending the auction at that price, then the auction has a right-censored observation because the bidder indicates that his or her willingness to pay is at or above the seller's specified price. Only 159 auctions (or about 4% of the 3830 auctions in our dataset) ended with a BuyItNow option being exercised. In 2002, another fixed price mechanism was introduced, under which the seller is simply allowed to list the item with a fixed price. Fixed-price listings also generate a right-censored observation and can be treated in the same way as the BuyItNow auctions. Because of these right- and left-censored observations, we estimate all specifications using Tobit maximum likelihood estimation with variable cutoff points. (24) Defining [Y.sub.i.sup.*] as the unobserved index variable for observation i with either a cutoff value from below [Y.sub.i.sup.o] (the opening insertion value) or above [Y.sup.b.sub.i] (either the BuyItNow or fixed price), and [Y.sub.i] as the observed random variable, we obtain

(1) [Y.sup.*.sub.i] = [X.sub.i][beta] + [[epsilon].sub.i

[Y.sub.i] = [Y.sub.i.sup.o] if [Y.sub.i.sup.o] > [Y.sup.*.sub.i]

(2) = Y.sup.b.sub.i] if [Y.sup.b.sub.i] < [Y.sup.*.sub.i]

= [Y.sup.*.sub.i] otherwise,

where [beta] is the vector of coefficients on [X.sub.i] and [[epsilon].sub.i] is the error term, assumed to be normally distributed with zero mean and constant variance [[sigma].sub.2]. The log-likelihood function l, or

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.],

is maximized over all i observations, where [PHI] is the cumulative standard normal distribution function and [phi] represents the normal distribution probability density function.

In addition, heteroscedasticity may be a problem because of the presence of observations collected on coins of different years and mint marks. Coins of different years and mint marks may come from distributions that differ in means and standard deviations. As noted above, we control for differences in means by including the current market coin value for each year and mint mark. To correct for heteroscedasticity, we estimate the model with the Huber-White estimation technique (Greene 2002).

To summarize, we examine the impact on Price of various channels of information transmission by presenting separate estimation results for all coins (I), for noncertified coins only (II), for certified coins only (III), and for noncertified coins with and without a visual description (IV). The separate estimations of noncertified coins, certified coins, and noncertified with and without a visual description allow us to analyze the impact of the seller's reputation in the presence of different information signaling mechanisms that affect the amount of uncertainty about coin quality. Our underlying hypotheses are that reputation matters but that the role of reputation increases with increased uncertainty about item-specific characteristics.

3. Estimation Results

Tables 2 to 5 report our estimation results (with robust standard errors in parentheses) for a number of different specifications. (25) Table 2 presents the results of the estimations performed on the entire dataset (I); Tables 3 and 4 contain results of estimations performed on noncertified (II) and certified (III) coins, respectively; and Table 5 presents results for noncertified coins with and without a visual description (IV). The various specifications (1 to 9) start with the simplest specification in which only reputational measures are included, and then progressively add other types of information signals and variables that capture features of the auctions.

Results in Table 2 for the entire dataset illustrate that Rating generally has a positive and statistically significant effect on the buyer's willingness to pay. (26) The average value for the lnRating coefficient across all specifications is 3.11. This magnitude suggests that for a seller with the average characteristics in the dataset (including an average Rating of 1889), one extra Rating point will increase willingness to pay by $0.17; similarly, a 10% increase in Rating will generate a $0.30 increase in the buyers' willingness to pay. While statistically significant, these impacts are clearly quite small. Given the average Price of coins in the full dataset (or $93.39), the 1 point increase in Rating represents a miniscule impact on the willingness to pay (or 0.2% of Price), and even the 10% increase in Rating increases the price by only 0.32%. Indeed, a doubling in the rating from 1889 to 3778 will increase the willingness to pay by only $2.18, or by 2.3% of Price.

Nevertheless, the difference in the buyers' willingness to pay between items auctioned by an established seller with a rating of 1889 and a newcomer with a rating of 0 is substantial, or $23.79 (or 25.5% of Price), and an extra rating point for the newcomer starting with a Rating of 0 will increase the willingness to pay by $2.19 (or 2.3% of Price).

Negative feedback also has effects on willingness to pay across the different specifications in Table 2. The coefficient on InNegative is consistently negative and statistically significant. Its magnitude is also much larger than on lnRating, which suggests that complaints are more important than (net) praises. (27) The average value of the 1nNegative coefficient across all nine specifications is -4.50, and the level of statistical significance is consistently above 95%. Given that the seller with average characteristics in the full dataset has slightly more than seven complaints, the cost of one additional complaint to the average seller is a reduction in $0.55 in buyers' willingness to pay, an impact that is much greater than the benefit from one extra positive comment. (28) Interestingly, a seller with the average Rating of 1889 and only 176 Negative comments will face the same willingness to pay as a newcomer with a Rating of 0 and no complaints. These results are consistent with most of the existing empirical investigations on the impact of a seller's reputation measures in eBay markets (Lucking-Reiley et al. 1999; Melnik and Alm 2002).

However, a seller's reputation appears to play a much more complicated role when a distinction is made between certified and noncertified coins. Table 3 presents estimation results for the subsample of noncertified coins. In all specifications of Table 3, the overall measure of the seller's reputation (Rating) has a positive and statistically significant impact on the buyer's willingness to pay, with an average coefficient of 2.89; given the lower average Price of noncertified coins, the relative impact of reputation is greater than for the full sample of coins in Table 2. (29) Further, the statistical significance of the overall reputation measure Rating now increases sharply, generally to the 99% confidence level or better. However, when certified coins are examined separately in Table 4, Rating is no longer a statistically significant determinant of willingness to pay. It therefore appears that the seller's reputation plays a significant role in the case of heterogeneous (e.g., noncertified) coins, and plays a much more limited role in the case of perfectly homogeneous (e.g., certified) coins.

As for other reputational measures, the results in Tables 3 and 4 also exhibit differences between noncertified and certified coins. In Table 3 (noncertified coins), the coefficient on Negative is statistically insignificant in all specifications. In Table 4 (certified coins), the coefficient is negative and statistically significant in all specifications. (30)

These results suggest that the two different measures of the seller's reputation may signal different aspects of seller's behavior to the bidder. The statistical significance of Rating in the case of noncertified coins and the absence of significance in the case of certified coins suggest that the overall reputational measure Rating may be interpreted by the bidder as a signal of reliability of the seller when it comes to the accuracy of the description of the item. In the case of noncertified coins, this signaling property is valued by the bidder; however, for certified coins any uncertainty about item-specific characteristics is largely removed by the certification, and the signaling property of Rating becomes irrelevant. In contrast, Negative may be interpreted as a signal about the reliability of the seller when it comes both to the delivery of the product and to compliance with the terms of transaction. Some evidence of this can be found in individual Negative feedback comments themselves. A large proportion of negative comments makes reference to the seller failing to deliver the product. This result may in part be due to the mechanism of feedback used on eBay. After a transaction, both the buyer and the seller have the opportunity to rate each other. In this setup, the buyer may be hesitant to leave a negative feedback because of a perceived expectation that the seller then would leave a negative retaliatory comment as well. Only when there is a major violation by the seller, such as the failure to deliver the item, is the buyer likely to leave negative feedback.

If Negative is viewed as a measure of the probability of encountering a fraudulent seller, then its magnitude and statistical importance should increase with the value of the item. Note that certified coins are much more expensive than noncertified coins ($327.50 versus $58.08). In the case of certified coins, the average magnitude of the coefficient on lnNegative in Table 4 is 39.23, while the average negative rating in auctions for certified coins is 10. Thus, the penalty that the buyer puts on a 1 point increase in a negative rating (from 10 to 11) is a decline in the buyer's willingness to pay by $3.74, which represents a 1.1% decline in the average price of certified coins in our dataset. In contrast, Negative does not have a statistically significant impact on Price in the case of noncertified coins.

The seller's neutral rating (Neutral) also has a differential impact on the buyer's willingness to pay in auctions for all coins, for noncertified coins, and for certified coins. However, the coefficient on lnNeutral is seldom statistically significant.

As for other information signals, the visual description of the coin may sometimes act as an important item-specific information signal. Nearly 80% of all auctions in the full dataset have a complete, two-sided scan of the coin, and a partial or one-sided scan is present in only 13% of the auctions. Starting with specification 3 in Tables 2 to 4, we include FullScan and PartialScan dummy variables. When the estimation is performed on the entire dataset (Table 2), the impact of these information signals is positive, as expected, but is also statistically insignificant. However, this result may be somewhat misleading because the dataset includes two different groups of coins, certified and noncertified coins, and the visual description could well play a different role for each of these groups. Indeed, a visual description would seem of more importance for noncertified coins than for certified coins. Tables 3 and 4 confirm this notion. In the case of noncertified coins (Table 3), both of these dummy variables have positive and statistically significant coefficients across most all specifications; for certified coins (Table 4), the coefficients on FullScan and PartiaIScan are never statistically significant. These results reinforce our earlier suggestion that the inclusion of an additional information signal is more important in auctions for goods that exhibit greater uncertainty about item-specific characteristics. It is also of interest that the inclusion of FullScan and PartialScan generally reduces the magnitude of the coefficient on lnRating, although not its statistical significance.

Similarly, the addition of dummy variables for acceptable methods of payment (PersonalCheck, OnlinePayment, CreditCard) tends to generate positive and statistically significant coefficients mainly in auctions for noncertified coins, and their addition reduces the impact of Rating. The inclusion of these additional information signals is important to buyers, but mainly in auctions for noncertified coins, and their inclusion reduces the role of reputation as an information signal.

To explore further the role of reputation, we report in Table 5 several specifications performed on auctions of noncertified coins. For noncertified coin auctions, scans are often but not always available, so in Table 5 we focus only on noncertified coins and, for comparative purposes, we do not include any of the scan variables in these specifications even when they are available. Specifications 1, 2, and 3 are for auctions of noncertified coins for which a visual description is available; specifications 4, 5, and 6 are for auctions where no visual description is available. For both types of coins, Rating has a positive and statistically significant impact on the buyer's willingness to pay. However, the average coefficient on lnRating for auctions with no visual scan (or in specifications 4, 5, and 6) is 4.87, nearly double the average magnitude for auctions with a visual scan (specifications 1, 2, and 3). For example, a 10% increase in the Rating of the average seller will increase the willingness to pay by 0.48% for auctions of noncertified coins with a visual description and by 0.84% for noncertified coins with no visual description. (31) Similarly, a 1-point increase in Rating (from 0 to 1) will increase the willingness to pay by 3.48% for noncertified coins with a visual description and by 6.12% for noncertified coins without a visual description. Further, Negative does not have a significant impact on Price in auctions for noncertified coins with scans, but plays an important role in auctions of noncertified coins with no scans. Note that the magnitude of the coefficient on Negative remains significantly lower for noncertified coins with no scans than for certified (and more expensive) coins where the penalty from encountering a dishonest seller is much higher. These results suggest that the seller's reputation plays a much smaller role in auctions where a visual scan allows the buyer to verify the quality of the coin by himself or herself. (32)

These reputational effects tend to be larger than those found in other studies that focused on relatively homogeneous goods. For example, Melnik and Alm (2002) find that a seller whose rating doubles (from 452 to 904) will increase willingness to pay for mint condition U.S. $5 coins by only 0.55%. Similarly, Houser and Wooders (2000) estimate that a 10% increase in the positive feedback will translate into an increase in the willingness to pay for a Pentium III, 500-MHz processor by only 0.17%, and Lucking-Reiley et al. (1999) estimate that a 1% gain in positive feedback will only lead to a 0.03% increase in willingness to pay for U.S. Indian head pennies in near mint state.

Overall, then our findings show that the impact of the seller's reputation on the buyer's willingness to pay depends on the degree of heterogeneity of the good in combination with the availability of other informational signals. In the case of certified coins, where uncertainty about item-specific characteristics is low, the seller's reputation has no statistically significant impact on the buyer's willingness to pay. However, in auctions of noncertified coins Rating has a positive and statistically significant impact on Price, and the magnitude of this impact increases further for auctions with no visual description of the coin.

The results for most other variables are generally consistent with expectations, although the coefficients on these variables are not always statistically significant. The coefficient on CoinValue is positive and statistically significant at above the 99% level in all specifications. The magnitude of its coefficient suggests that a $1 increase in the market value of the coin will generate an increase in the willingness to pay but only by $0.25 in the case of noncertified coins (Table 3) and by $0.28 in the case of certified coins (Table 4).

Another important feature of an auction is the list of acceptable methods of payment. Methods of payment influence transactions costs, and so may affect buyers' willingness to pay for the item. In fact, the empirical results in specifications 4 and above in Table 2 to 4 are largely consistent with this notion. Acceptance of a personal check as a payment method has a positive and statistically significant impact on auctions of noncertified coins, while the effect on auctions of certified coins is statistically insignificant. The use of online payment methods has statistically insignificant impacts on willingness to pay. (33) As for credit cards, direct acceptance of credit cards by the seller has a positive and statistically significant impact on Price but only in auctions for noncertified coins. Credit card acceptance may be yet another mechanism that can signal to the buyer whether the seller has an established business or not.

Specification 6 introduces more precise measures of the grades. (34) The signs of the coefficients on the numerical grade measure dummy variables are generally consistent with expectations because the dummy variables on the lower quality coins graded AU-50, AU-53, and AU-55 have negative coefficients in Table 2 and the dummy variable on the higher quality coin (e.g., AU-58 grade coins) has a positive coefficient. (35) However, these coefficients are seldom statistically significant (with the exception of AU-50 in Table 3). Note that the inclusion of numerical grade variables does not have a significant impact on the magnitude or statistical significance of the coefficients on the reputation measures.

We also include the effects of the time and day of the week of the closing of the auction on the willingness to pay. Specification 7 in Tables 2 to 4 includes dummy variables for the day of the week. The results indicate that auctions that close on Saturdays and Sundays generate a higher price in the case of noncertified coins (Table 3). However, day of the week plays a less important role in the case of certified coins (Table 4), where only the coefficient on Thursday is statistically significant. As can be seen from the number of observations, certified coins are far more limited, and the closing date may be less important in the determination of winning bids. This can also be seen in the coefficients on the closing time variables, two of which are statistically significant in the case of noncertified coins but none of which is significant in the case of certified coins. The statistical significance of these dummy variables in the case of noncertified coins offers support to the notion that at least some auctions receive more attention from bidders in their closing states. Auctions closing between midnight and 6 AM will appear at the top of the search results of perspective bidders during the evening hours of the previous day.

It may well be that fluctuations in supply are in part responsible for daily fluctuations in prices. To investigate this, CoinFrequency is also included in some specification. Recall that CoinFrequency is equal to the number of identical coin auctions closing on the same day. Its coefficient has a negative and statistically significant coefficient in most all specifications in Tables 2 to 4. However, even controlling for the supply of coins on a given day of the week, we find that coins sold on Saturday and Sunday command higher winning bids, something that suggests an increased bidder activity on nonworking days.

Many previous econometric studies of auctions have attempted to control for the length of the auction. The length of the auction is measured in the specification by dummy variables for 5-, 7-, and 10-day auctions, with the control group consisting of 3-day auctions. (36) The coefficient on 10-day auctions is positive and only marginally significant, while the coefficients on 7- and 5-day auctions are statistically insignificant. Recall that auctions near their closing time tend to be more visible to the perspective bidders because search results can be sorted via the default option by the remaining auction time; given the large number of Morgan dollar coins listed on eBay at any given time, it is likely that bidders limit their search to those auctions that are near completion, and this will reduce the impact of the duration of the auction on the realized price.

4. Conclusions

It is clear that buyers value information in online auctions. However, the value that buyers place on any one information mechanism seems to fall as the number of information signals increases. For example, a seller's overall reputation often has a positive and statistically significant impact on willingness to pay, a result that is consistent with reputation playing an important role in signaling the quality of item-specific characteristics in the auctions of heterogeneous goods. Similarly, a measure of complaints about the seller (Negative) also has an important--and negative--impact on willingness to pay, and may be interpreted by the buyer as the measure of the probability that the seller is fraudulent. However, the reputational effects of Rating tend to be of greater importance for more heterogeneous goods (e.g., noncertified coins and coins without a visual scan), where it is more difficult for buyers to verify independently the quality of the good, while Negative comments largely affect a buyer's willingness to pay for more homogeneous and more expensive goods (e.g., certified coins). These reputational effects are also sensitive to the presence of other information signals about the item-specific characteristics of the good, such as the availability of online payment mechanisms that may give some indication of seller reliability. For example, seller acceptance of credit card payment has a positive and statistically significant impact on price for noncertified coins, but not for certified coins.

The buyer's interpretation of a seller's previous reputation as a signal about the current behavior of the seller in online auctions reinforces the notion that measures of sellers' reputation can reduce the problem of asymmetric information in online auctions. However, it is also important to note that no uniform measures of reputation exist in online commerce today, and proprietary measures of reputation such as the eBay rating mechanism are not transferable to other Web sites; indeed, eBay has gone to court to maintain its reputation measures as its own. Although our results suggest that any such measures help to reduce the problem of asymmetric information in online auctions, these measures may also help to erect barriers to entry for new auction Web sites because their existence can establish a barrier to entry for new auction Web sites by making it costly for established sellers to switch from one auction Web site to another. Consequently, there may be a need for a uniform and universal measure of online reputation, a measure that is maintained by some other agency than the auction Web site and that is transferable across Web sites.

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(1) See Dellarocas (2003) and Bajari and Hortacsu (2004) for recent surveys of many of these empirical studies. There is also some empirical work on reputation impacts outside of e-commerce. For example, Landon and Smith (1998) examine the impact of reputation on the price of Bordeaux wines.

(2) For a more detailed description of Internet auction mechanisms, see Lucking-Reiley (2000).

(3) eBay user statistics are available on the eBay Web site at http://investor.ebay.com/index.cfm.

(4) For instance, in cases where personal checks are accepted, sellers typically require a check clearing period that can range between 5 and 14 days before the good is shipped. In the case of credit card or online payment methods, the shipping occurs following the completion of the payment.

(5) The seller can also post comments about the buyer.

(6) These comments are easily accessible in the feedback section for each member of eBay.com.

(7) Note that not all auctions listed on the eBay Web site complete successfully. Auctions where insertion price exceeds buyer's willingness to pay receive no bids.

(8) In contrast, Eaton (2002) and Resnick et al. (2002) fail to find a statistically significant impact of the seller's reputation on the realized price; however, they do find a positive effect of reputation on the probability of a successful completion of the auction. Two controlled experimental studies have been done as well. Katkar and Lucking-Reiley (2000) focus on the effects of reserve prices on willingness to pay, using reputation as a control variable, and Resnick and Zeckhouser (2002) find that an established seller receives a price premium of 7.6% over a newcomer. For a recent overview of existing empirical literature on the effects of reputational measures in online auctions, see Bajari and Hortacsu (2004).

(9) Lucking-Reiley et al. (1999) use coins in near mint state condition with precisely defined grades. Although they do not provide any information on whether the coins received any third party grading, such precise grade assignments tend to be assigned by professional grading services.

(10) A recent exception is Eaton (2002), who finds the impact of reputation on the realized price to be statistically insignificant in eBay auctions for PRS guitars.

(11) Houser and Wooders (2000) show that in equilibrium the buyer with the highest expected value of winning the auction wins the auction and pays the expected value of the buyer with the second highest value. This expected value is given by [b.sub.2] = [r.sup.S][v.sub.2], where [b.sub.2] is the second-highest bid, [r.sub.s] is the reputation score of the seller, and [v.sub.2] is the value of the good to the second-highest bidder.

(12) For example, the 1883-S dollar in AU condition has the catalog value of $175, while in just one grade lower (EF) the same coin is valued at only $45.

(13) The Standard catalog of world coins (Krause and Mishler 2001) defines AU coins as coins where "all detail will be visible. There will be wear only on the highest point of the coin. There will often be half or more of the original mint luster present."

(14) As a sign of their popularity among collectors, the Professional Coin Grading Services (PCGS), one of the leading coin grading companies, lists market values for all Morgan dollar coins on its Web site. The PCGS Web site can be found at http://www.pcgs.com.

(15) Note that our dataset excludes observations where the coin was previously cleaned. Cleaned coins are not as valuable as coins that contain their original patina. Auctions where the seller stated that the coin had been cleaned were not included in our dataset because there is no corresponding catalog value that would allow us to have an adequate control for the catalog valuation of those coins.

(16) eBay uses a proxy bidding system. The highest bidder in an auction wins the auction, and pays a price equal to the price bid by the second highest bidder plus a bid increment.

(17) Note that all certified coins are supposed to receive a precise numerical grade. However, for 10 observations of certified coins in our dataset the seller failed to state the numerical grade category. These 10 observations are excluded from all specifications that use dummy variables with numerical grades.

(18) We are grateful to an anonymous referee for this suggestion.

(19) The "mint mark" designates the mint (or place) where the coin was minted. Four unique mints are present in the dataset.

(20) The PCGS provides coin values for AU category broadly defined and not for individual numerical categories such as AU-50. Thus, the dummy coefficients on individual numerical grade categories (when included) represent the difference in willingness to pay as expressed by eBay bidders between that numerical grade category and the "average" AU grade.

(21) These methods of payment enable the buyer to submit the payment online. They allow the seller to accept credit cards and, in the case of PayPal, bank transfers. With the exception of BidPay, which imposes a money order fee on the buyer, these services are free to buyers; however, sellers are typically required to pay a fraction of the received payment in fees if the payment is made with a credit card. In each instance, the seller is notified via E-mail as soon as the payment is made, thereby expediting the shipment of the item. Note that Billpoint no longer exists.

(22) Ideally, we would like to estimate a complete two-equation model of the demand for and supply of coins. Unfortunately, however, we do not have sufficient information that would allow us to specify the supply of coins. Although the inclusion of CoinFrequency captures some supply considerations, we recognize that this variable is likely to be an imperfect reflection of all supply factors. We are grateful to an anonymous referee for this observation.

(23) We have also estimated specifications that include the minimum bid, as in Lucking-Reiley et al. (1999). The coefficient on the minimum bid is never statistically significant, and its presence does not affect the sign, magnitude, or statistical significance of the other coefficients.

(24) See Amemiya (1984) for a detailed discussion of this estimation method.

(25) As discussed by Amemiya (1984), the estimated coefficient [[beta].sub.i] for independent variable [X.sub.i] gives the impact of the independent variable on the unobserved index variable [Y.sub.i.sup.*], or what might be termed the willingness to pay for the good. The impact of [X.sub.i] on the actual observed variable [Y.sub.i] (or, equivalently, [Price.sub.i]) is given by [differential]E[[Y.sub.i] | [X.sub.i]]/[differential][X.sub.i] = [beta]'[[PHI]([Y.sub.i.sup.b] - [beta][X.sub.i]/[sigma]) - [PHI]([Y.sub.i.sup.o] - [beta][X.sub.i]/[sigma])], where E is the expectation operator.

(26) In specification 6, the coefficient on lnRating is statistically significant only at the 88.4% confidence level.

(27) Recall that Rating is constructed as the difference between praises and complaints left by unique users with whom the seller had transaction experience.

(28) When computing the effects of a change in the Negative rating, we keep the level of the overall Rating constant.

(29) The average price of certified coins is $327.50, and that of noncertified coins is $58.08. The average price of all coins in the full sample is $93.39.

(30) Direct comparison of the coefficients across Tables 3 and 4 should be done cautiously because of differences in the distributions of Rating and Negative between the sellers of the two categories of coins.

(31) Percent changes are computed based on the average prices of coins in each of the two categories. The average price for noncertified coins with a visual description is $58.34 and is $55.13 for noncertified coins with no visual description.

(32) It should be noted that there may be an issue with self-selection here because the presence of a scan does not indicate the quality of the coin but merely enables the buyers to examine the coin for themselves; for coins with low quality, the presence of a scanned image may actually reduce the price. In fact, sellers with low quality coins have little incentive to provide a scanned image.

(33) Direct acceptance requires that the seller be equipped to take payments directly from Visa, MasterCard, or other credit cards; online methods of payment such as PayPal and Billpoint enable the buyer to pay with a credit card but through a third party.

(34) Specifications restricted to certified coins omit AU-50 grade category. In the case of noncertified coins, many coins simply have AU as the grade, which acts as the omitted category in Tables 2 and 3, but all certified coins will have a numerical grade, thus AU-50 is selected as the reference group. This also implies that the coefficient on Certified in specification 6 in Table 2 is not identified.

(35) As noted earlier, for 10 observations on certified coins we have no information on the numerical grade of the coin. For this reason, specification 6 excludes those 10 observations.

(36) Auctions that close with an exercise of the BuyItNow option must be excluded from this last specification because they do not last a predetermined period.

Mikhail I. Melnik * and James Alm ([dagger])

* Department of Economics, Andrew Young School of Policy Studies, Georgia State University, P.O. Box 3992, Atlanta, GA 30302-3992 USA; E-mail: prcmxmx@langate.gsu.edu.

([dagger]) Department of Economics, Andrew Young School of Policy Studies, Georgia State University, P.O. Box 3992, Atlanta, GA 30302-3992 USA; E-mail: jalm@gsu.edu; corresponding author.

We are grateful to Laura Razzolini and to two anonymous referees for many helpful comments.

Received July 2002; accepted April 2005.

Table 1. Descriptive Statistics

 All Coins Noncertified Coins

 Mean Mean
Variable (Standard Deviation) (Standard Deviation)

Price 93.393 (355.50) 58.080 (111.874)
CoinValue 182.885 (932.087) 112.159 (271.652)
Rating 1889.198 (2384.371) 1877.787 (2476.495)
Negative 7.451 (15.513) 7.026 (14.843)
Neutral 11.454 (22.916) 11.586 (23.940)
Length 6.578 (1.895) 6.511 (1.909)
Certified 0.131 --
10-Day 0.117 0.111
7-Day 0.622 0.613
5-Day 0.143 0.147
AU-50 0.143 0.102
AU-53 0.040 0.020
AU-55 0.079 0.064
AU-58 0.092 0.072
PersonalCheck 0.892 0.889
OnlinePayment 0.770 0.768
CreditCard 0.114 0.083
FullScan 0.786 0.777
PartialScan 0.134 0.141
Sunday 0.223 0.220
Saturday 0.196 0.209
Friday 0.110 0.110
Thursday 0.134 0.138
Wednesday 0.103 0.100
Tuesday 0.126 0.125
Monday 0.108 0.099
CoinFrequency 12.348 (9.706) 12.104
Time 0-6 0.027 0.029
Time 6-12 0.177 0.177
Time 12-18 0.396 0.419
Time 18-24 0.400 0.376

 Certified Coins

 Mean
Variable (Standard Deviation)

Price 327.500 (905.301)
CoinValue 651.761 (2428.235)
Rating 1964.845 (1648.103)
Negative 10.267 (19.157)
Neutral 10.582 (14.375)
Length 7.020 (1.737)
Certified --
10-Day 0.157
7-Day 0.681
5-Day 0.116
AU-50 0.412
AU-53 0.167
AU-55 0.175
AU-58 0.225
PersonalCheck 0.912
OnlinePayment 0.779
CreditCard 0.472
FullScan 0.847
PartialScan 0.088
Sunday 0.245
Saturday 0.112
Friday 0.108
Thursday 0.108
Wednesday 0.124
Tuesday 0.133
Monday 0.171
CoinFrequency 13.968 (11.011)
Time 0-6 0.014
Time 6-12 0.179
Time 12-18 0.241
Time 18-24 0.566

Table 2. Estimation Results I--All Coins

 Specification
Independent
Variable 1 2 3

LnRating 2.573 *** 3.749 ** 3.864 **
 (0.825) (1.642) (1.764)
LnNegative -3.826 ** -5.336 ***
 -1.740 -1.873
LnNeutral 1.139 1.764
 -2.433 -2.594
CoinValue 0.287 *** 0.287 *** 0.285 ***
 (0.034) (0.034) (0.035)
Certified 35.158 ***
 (6.671)
FullScan 3.067
 (3.926)
PartialScan 11.697
 (7.735)
PersonalCheck
OnlinePayment
CreditCard
CoinFrequency
AU-50
AU-53
AU-55
AU-58
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Time 0-6
Time 6-12
Time 18-24
10-Day
7-Day
5-Day
Constant 4.332 -0.318 -7.888
 (6.635) (9.846) (10.036)
Chi-square 82.05 94.26 280.82
Degrees of freedom 2 4 7
Observations 3828 3828 3828

 Specification
Independent
Variable 4 5 6

LnRating 3.201 * 3.011 * 2.64
 (1.725) (1.716) (1.690)
LnNegative -4.967 *** -4.368 ** -3.95 **
 -1.878 -1.850 -1.773
LnNeutral 1.406 1.086 1.253
 -2.641 -2.628 -2.710
CoinValue 0.285 *** 0.284 *** 0.284 ***
 (0.035) (0.035) (0.035)
Certified 35.698 *** 37.806 *** 38.865 ***
 (7.510) (7.567) (7.424)
FullScan 3.391 4.351 5.140
 (4.330) (4.350) (4.411)
PartialScan 11.539 10.813 10.114
 (7.825) (7.820) (7.596)
PersonalCheck 9.562 *** 9.707 *** 9.804 ***
 (3.563) (3.566) (3.596)
OnlinePayment 1.198 1.449 0.883
 (3.979) (3.952) (3.996)
CreditCard -0.959 -1.231 -1.769
 (4.671) (4.664) (4.964)
CoinFrequency -0.829 *** -0.804 ***
 (0.111) (0.109)
AU-50 -7.167
 (5.371)
AU-53 -7.043
 (17.871)
AU-55 -0.159
 (4.594)
AU-58 9.435
 (6.420)
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Time 0-6
Time 6-12
Time 18-24
10-Day
7-Day
5-Day
Constant -12.891 -2.743 -1.354
 (11.174) (11.296) (11.259)
Chi-square 311.97 332.14 350.36
Degrees of freedom 10 11 15
Observations 3828 3828 3818

 Specification
Independent
Variable 7 8 9

LnRating 2.871 * 3.055 * 3.054 *
 (1.664) (1.790) (1.740)
LnNegative -4.144 ** -4.801 ** -4.625 **
 -1.922 -1.994 -1.824
LnNeutral 1.181 1.541 2.907
 -2.746 -2.691 -2.396
CoinValue 0.284 *** 0.284 *** 0.284 ***
 (0.035) (0.035) (0.035)
Certified 39.061 *** 39.353 *** 36.333 ***
 (7.319) (7.497) (6.579)
FullScan 2.442 3.141 1.842
 (4.548) (4.648) (3.851)
PartialScan 9.899 10.617 4.435
 (7.780) (7.819) (6.945)
PersonalCheck 9.884 8.821
 (3.551) (3.565)
OnlinePayment 1.095 0.891
 (3.919) (3.686)
CreditCard -1.480 -1.716
 (4.814) (4.907)
CoinFrequency -0.958 *** -0.961 ***
 (0.124) (0.124)
AU-50
AU-53
AU-55
AU-58
Tuesday 0.431 0.484
 (5.167) (5.167)
Wednesday 7.757 7.676
 (6.931) (6.967)
Thursday -0.045 -0.534
 (4.641) (4.571)
Friday 3.991 3.201
 (4.809) (4.752)
Saturday 9.723 ** 8.440 *
 (4.403) (4.449)
Sunday 10.041 * 10.661
 (5.567) (5.539)
Time 0-6 24.954 ***
 (7.663)
Time 6-12 9.001 **
 (3.739)
Time 18-24 4.173
 (4.667)
10-Day 5.598
 (6.050)
7-Day 4.483
 (3.102)
5-Day 0.506
 (4.153)
Constant -4.435 -10.157 -11.446
 (12.348) (13.506) (9.998)
Chi-square 421.44 489.11 375.11
Degrees of freedom 17 20 10
Observations 3828 3828 3828

* Statistically significant at 90% and above.

** Statistically significant at 95% and above.

*** Statistically significant at 99% and above.

Table 3. Estimation Coins Only Results II--Noncertified

 Specification
Independent
Variable 1 2 3

LnRating 2.497 *** 3.946 *** 3.432 ***
 (0.695) (1.115) (1.162)
LnNegative -0.522 -0.573
 (1.528) (1.523)
LnNeutral -1.833 -1.090
 (1.434) (1.514)
CoinValue 0.251 *** 0.252 *** 0.251 ***
 (0.031) (0.032) (0.032)
FullScan 9.812 ***
 (2.004)
PartialScan 5.885 **
 (2.825)
PersonalCheck
OnlinePayment
CreditCard
CoinFrequency
AU-50
AU-53
AU-55
AU-58
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Time 0-6
Time 6-12
Time 18-24
10-Day
7-Day
5-Day
Constant 2.848 -3.386 -9.432
 (4.495) (6.194) (6.358)
Chi-square 96.09 103.42 168.49
Degrees of freedom 2 4 6
Observations 3328 3328 3328

 Specification
Independent
Variable 4 5 6

LnRating 2.904 *** 2.854 *** 2.567 **
 (1.115) (1.101) (1.116)
LnNegative -0.342 0.319 0.682
 (1.551) (1.507) (1.485)
LnNeutral -1.813 -2.394 -2.372
 (1.562) (1.547) (1.544)
CoinValue 0.251 *** 0.252 *** 0.252 ***
 (0.032) (0.032) (0.032)
FullScan 9.055 *** 9.455 *** 9.902 ***
 (2.132) (2.169) (2.197)
PartialScan 6.159 ** 5.427 * 5.278 *
 (2.829) (2.833) (2.847)
PersonalCheck 6.927 ** 6.716 * 6.851 *
 (3.499) (3.520) (3.525)
OnlinePayment 3.334 3.845 3.621
 (2.886) (2.896) (2.854)
CreditCard 9.021 ** 10.073 *** 9.130 **
 (3.543) (3.534) (3.684)
CoinFrequency -0.729 *** -0.725 ***
 (0.128) (0.127)
AU-50 -7.173 **
 (3.299)
AU-53 5.436
 (6.466)
AU-55 0.072
 (4.886)
AU-58 4.567
 (4.984)
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Time 0-6
Time 6-12
Time 18-24
10-Day
7-Day
5-Day
Constant -13.969 ** -5.443 -3.998
 (7.135) (6.863) (6.885)
Chi-square 221.73 235.09 267.96
Degrees of freedom 9 10 14
Observations 3328 3328 3328

 Specification
Independent
Variable 7 8 9

LnRating 2.512 ** 2.690 *** 2.592 **
 (1.086) (1.076) (1.175)
LnNegative 0.351 0.067 -0.277
 (1.530) (1.552) (1.519)
LnNeutral -2.019 -2.117 -0.01
 (1.555) (1.561) (1.457)
CoinValue 0.251 *** 0.251 *** 0.246 ***
 (0.032) (0.032) (0.032)
FullScan 8.351 *** 8.787 *** 8.999 ***
 (2.190) (2.284) (1.891)
PartialScan 5.184 * 5.609 * -0.121
 (2.919) (3.014) (2.319)
PersonalCheck 6.711 * 6.596 *
 (3.537) (3.534)
OnlinePayment 3.299 3.355
 (2.923) (2.919)
CreditCard 9.142 ** 8.812 **
 (3.791) (3.902)
CoinFrequency -0.890 *** -0.881 ***
 (0.141) (0.143)
AU-50
AU-53
AU-55
AU-58
Tuesday 3.972 3.819
 (4.558) (4.566)
Wednesday 7.732 8.092 *
 (4.894) (4.873)
Thursday 5.456 5.340
 (3.812) (3.780)
Friday 5.188 4.829
 (4.169) (4.073)
Saturday 14.309 *** 14.153 ***
 (3.511) (3.581)
Sunday 12.868 *** 13.742 ***
 (3.964) (3.999)
Time 0-6 15.051 ***
 (4.564)
Time 6-12 5.577 *
 (3.349)
Time 18-24 -2.108
 (2.463)
10-Day 7.802
 (5.044)
7-Day 3.080
 (1.082)
5-Day -0.809
 (3.394)
Constant -8.869 (10.396) -9.626
 (7.309) (7.482) (6.865)
Chi-square 242.50 301.03 214.29
Degrees of freedom 16 19 9
Observations 3328 3328 3178

* Statistically significant at 90% and above.

** Statistically significant at 95% and above.

*** Statistically significant at 99% and above.

Table 4. Estimation Results III--Certified Coins Only

 Specification
Independent
Variable 1 2 3

LnRating -3.005 -4.588 1.323
 (4.087) (12.269) (10.594)
LnNegative -43.119 *** -38.537 **
 (12.952) (15.823)
LnNeutral 45.119 * 41.149 *
 (24.607) (23.916)
CoinValue 0.287 *** 0.285 *** 0.283 ***
 (0.037) (0.038) (0.037)
FullScan -10.258
 (31.759)
PartialScan 95.502
 (76.416)
PersonalCheck
OnlinePayment
Credit
CoinFrequency
AU-53
AU-55
AU-58
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Time 0-6
Time 6-12
Time 18-24
10-Day
7-Day
5-Day
Constant 71.723 ** 74.831 35.058
 (28.685) (49.709) (45.551)
Chi-square 60.86 137.91 138.61
Degrees of freedom 2 4 6
Observations 500 500 500

 Specification
Independent
Variable 4 5 6

LnRating -1.208 -2.135 -2.852
 (11.305) (11.313) (13.310)
LnNegative -38.312 ** -39.709 ** -39.697 **
 (17.147) (17.142) (17.794)
LnNeutral 40.897 43.866 * 44.415
 (25.699) (25.594) (28.417)
CoinValue 0.282 *** 0.280 *** 0.281 ***
 (0.037) (0.038) (0.038)
FullScan -2.791 8.650 7.138
 (38.732) (41.839) (44.291)
PartialScan 93.661 100.307 91.808
 (77.057) (76.196) (74.211)
PersonalCheck 17.879 23.441 23.062
 (23.472) (25.264) (24.728)
OnlinePayment -26.373 -29.019 -29.789
 (28.150) (28.770) (31.277)
Credit 1.691 -4.807 -3.804
 (18.563) (19.788) (20.653)
CoinFrequency -1.554 ** -1.439 **
 (0.727) (0.726)
AU-53 -19.777
 (38.070)
AU-55 2.063
 (16.017)
AU-58 24.180
 (25.555)
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Time 0-6
Time 6-12
Time 18-24
10-Day
7-Day
5-Day
Constant 51.629 68.180 69.461
 (51.151) (52.119) (72.120)
Chi-square 186.58 239.67 286.06
Degrees of freedom 9 10 13
Observations 500 500 490

 Specification
Independent
Variable 7 8 9

LnRating -2.080 -0.797 3.474
 (11.816) (12.178) (10.381)
LnNegative -38.519 ** -40.876 ** -35.906 *
 (18.150) (17.240) (14.981)
LnNeutral 42.376 39.407 38.906 *
 (26.805) (27.388) (21.864)
CoinValue 0.281 *** 0.281 *** 0.283 ***
 (0.037) (0.037) (0.037)
FullScan -1.419 4.013 -18.120
 (42.570) (40.879) (33.721)
PartialScan 92.665 106.948 99.543
 (75.960) (80.194) (76.972)
PersonalCheck 21.808 16.040
 (26.913) (29.789)
OnlinePayment -32.679 -30.794
 (29.550) (25.494)
Credit -11.758 -18.191
 (22.567) (22.657)
CoinFrequency -0.987 -0.943
 (0.618) (0.609)
AU-53
AU-55
AU-58
Tuesday -27.422 -30.954
 (24.665) (26.144)
Wednesday 16.824 11.094
 (30.686) (29.440)
Thursday -40.136 ** -49.050 **
 (17.977) (19.350)
Friday -10.319 -12.267
 (17.403) (17.464)
Saturday -23.088 -28.569
 (26.199) (26.125)
Sunday -36.902 -44.072
 (29.249) (28.618)
Time 0-6 -32.205
 -48.737
Time 6-12 47.004
 -34.004
Time 18-24 54.180
 -35.285
10-Day 9.673
 -28.432
7-Day 26.329
 -28.432
5-Day -2.576
 -40.487
Constant 95.100 61.752 -0.129
 (50.827) (57.323) (58.130)
Chi-square 395.01 511.37 392.75
Degrees of freedom 16 19 9
Observations 500 500 493

* Statistically significant at 90% and above.

** Statistically significant at 95% and above.

*** Statistically significant at 99% and above.

Table 5. Estimation Results IV-Noncertified Coins Only with and
without Scans

 Noncertified Coins with Scans
Independent
Variable 1 2 3

LnRating 3.511 *** 2.869 *** 2.391 **
 (1.170) (1.142) (1.123)
LnNegative -0.045 0.207 1.104
 (1.587) (1.614) (1.586)
LnNeutral -1.303 -2.004 -2.247
 (1.500) (1.545) (1.550)
CoinValue 0.253 *** 0.254 *** 0.254 ***
 (0.033) (0.033) (0.033)
PersonalCheck 7.272 ** 6.958 *
 (3.639) (3.687)
OnlinePayment 3.555 3.606
 (3.009) (3.107)
CreditCard 8.406 ** 8.409 **
 (3.583) (3.845)
CoinFrequency -0.950 ***
 (0.149)
Tuesday 4.068
 (4.918)
Wednesday 8.287
 (5.116)
Thursday 4.057
 (4.168)
Friday 5.292
 (4.370)
Saturday 14.761 ***
 (3.633)
Sunday 13.819 ***
 (4.177)
Constant -1.232 -6.078 -0.797
 (6.575) (7.175) (7.363)
Chi-square 102.52 143.19 164.24
Degrees of freedom 4 7 14
Observations 3059 3059 3059

 Noncertified Coins without Scans
Independent
Variable 4 5 6

LnRating 4.960 *** 4.626 *** 5.016 ***
 (1.391) (1.311) (1.354)
LnNegative -5.364 * -7.419 ** -9.959 ***
 (2.844) (3.177) (3.401)
LnNeutral -0.984 0.372 1.978
 (2.929) (2.983) (2.978)
CoinValue 0.194 *** 0.195 *** 0.195 ***
 (0.033) (0.032) (0.032)
PersonalCheck -0.294 0.764
 (2.729) (2.822)
OnlinePayment 5.763 * 5.794 *
 (3.132) (3.040)
CreditCard 26.082 *** 27.377 ***
 (8.592) (8.926)
CoinFrequency 0.086
 (0.198)
Tuesday 5.436
 (6.659)
Wednesday 8.812
 (7.831)
Thursday 5.345
 (6.424)
Friday 12.292 *
 (7.264)
Saturday 10.820
 (6.751)
Sunday 13.720
 (8.557)
Constant -9.938 -11.938 -23.234 **
 (6.500) (7.422) (9.952)
Chi-square 62.03 73.08 92.21
Degrees of freedom 4 7 14
Observations 269 269 269

* Statistically significant at 90% and above.

** Statistically significant at 95% and above.

*** Statistically significant at 99% and above.